We are given a box-and-whisker plot representing the masses of parcels in a van. We need to find the median, the interquartile range, and describe the effect of removing two parcels of specific masses (2.4 kg and 5.8 kg) on the median of the remaining parcels.

1. Problem Description

We are given a box-and-whisker plot representing the masses of parcels in a van. We need to find the median, the interquartile range, and describe the effect of removing two parcels of specific masses (2.4 kg and 5.8 kg) on the median of the remaining parcels.

2. Solution Steps

(i) Find the median:

The median is represented by the line inside the box of the box-and-whisker plot.

From the plot, the median appears to be at approximately 4.3 kg.

(ii) Find the interquartile range:

The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1).

From the plot, the upper quartile (Q3) is at approximately 5.9 kg.

The lower quartile (Q1) is at approximately 1.5 kg.

$IQR = Q3 - Q1$

$IQR = 5.9 - 1.5 = 4.4$

(iii) Effect of removing two parcels on the median:

The two parcels removed have masses 2.4 kg and 5.8 kg.

Since the median is 4.3 kg, one parcel (2.4 kg) is below the median, and one parcel (5.8 kg) is above the median.

Removing one value below the median and one value above the median means that the median will not change significantly. It might change slightly depending on the exact distribution of the data but it will be closer to the new center of the data. Since we are removing data points on either side of the original median, we could estimate the median will stay roughly the same. The median will slightly increase because the parcel removed at 2.4kg is closer to the 0 end than the parcel removed at 5.8kg.

3. Final Answer

(i) 4.3 kg

(ii) 4.4 kg

(iii) The median will slightly increase. Removing a value of 2.4 kg (below the median) and a value of 5.8 kg (above the median) skews the data towards a higher median.